Problem: The following line passes through point $(3, -3)$ : $y = -\dfrac{4}{5} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(3, -3)$ into the equation gives: $-3 = -\dfrac{4}{5} \cdot 3 + b$ $-3 = -\dfrac{12}{5} + b$ $b = -3 + \dfrac{12}{5}$ $b = -\dfrac{3}{5}$ Plugging in $-\dfrac{3}{5}$ for $b$, we get $y = -\dfrac{4}{5} x - \dfrac{3}{5}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(3, -3)$